Let \( r \) represent the total number of residents surveyed. According to the information provided, two-fifths of the respondents like spending their vacation at the beach, and this number is given as 80 residents. We can set up the equation based on this information:
\[ \frac{2}{5} r = 80 \]
To find the total number of residents surveyed, \( r \), we can solve this equation. First, we can multiply both sides by 5 to eliminate the fraction:
\[ 2r = 80 \times 5 \]
Calculating the right side:
\[ 2r = 400 \]
Now we can divide both sides by 2 to solve for \( r \):
\[ r = \frac{400}{2} \] \[ r = 200 \]
So, the total number of residents surveyed is \( \boxed{200} \).